We present optical and near-IR observations of the host galaxy of GRB 020127, for which we measure R-Ks=6.2 mag. This is only the second GRB host to date classified as an ERO. The spectral energy distribution (SED) is typical of a dusty starburst galaxy, with a redshift z~1.9, a luminosity L~5L*, and an inferred stellar mass of M*~1011-1012 Msolar, two orders of magnitude more massive than typical GRB hosts. A comparison to the z~2 mass-metallicity (M-Z) relation suggests that the host metallicity is about 0.5-1Zsolar. This result shows that at least some GRBs occur in massive, metal-enriched galaxies, and that the proposed low-metallicity bias of GRB progenitors is not as severe as previously claimed. Instead, we propose that the blue colors and sub-L* luminosities of most GRB hosts reflect their young starburst populations. This explanation also accounts for the prevalence of low-redshift GRBs in low-mass galaxies, since star formation activity shifts from high- to low-mass galaxies as a function of decreasing redshift (``downsizing''). Thus, the low-metallicity bias claimed for z<~0.2 GRB hosts is likely a secondary effect, which reflects the M-Z relation, and consequently GRBs and their hosts may serve as a reliable tracer of cosmic star formation activity.